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ANALYSIS OF GATE 2021
Computer Science Engineering
Engineering Mathematics
9% Digital Logic5%
Operating System (OS)6%
Theory of Computation
8%
Computer Organization and
Architecture6%
Discrete Mathematics & Graph Theory
8%
Programming and Data Structures
8%
Algorithms11%
DBMS8%
Compiler Design7%
Computer Networks9%
General Aptitude15%
Memory Based
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CS ANALYSIS-2021_Feb-13_ Morning
SUBJECT No. of Ques. Topics Asked in Paper (Memory Based) Level of
Ques. Total Marks
Engineering Mathematics
1 Marks: 1
2 Marks: 4 PDF, limits, Eigen values and vectors
Matrix
Moderate to
Difficult 9
Digital Logic 1 Marks: 1
2 Marks: 2 Synchronous circuit, Number system Easy 5
Operating System (OS)
1 Marks: 4
2 Marks: 1 Process Synchronous, Scheduling
Algorithm
Moderate to
Difficult 6
Theory of Computation
1 Marks: 2
2 Marks: 3
DFA, push down automata, decidability and undecidability, CFL and regular
language Medium 8
Computer Organization and
Architecture
1 Marks: 2
2 Marks: 2
Pipeline, memory organization addressing modes, floating point
representation Medium 6
Discrete Mathematics & Graph Theory
1 Marks: 2
2 Marks: 3 Groups, Graphs, Combinatorics Medium 8
Programming and Data Structures
1 Marks: 2
2 Marks: 3 Function, stack and queue Medium 8
Algorithms 1 Marks: 7
2 Marks: 2 Spanning tree, Asymptotic notation Medium 11
Database Management
System
1 Marks: 2
2 Marks: 3 Relational algebra Medium 8
Compiler Design 1 Marks: 1
2 Marks: 3 SDT, code optimization Easy 7
Computer Networks
1 Marks: 1
2 Marks: 4 Transport layer, network layer Medium 9
General Aptitude 1 Marks: 5
2 Marks: 5
Geometry, Probability, Word analogy, Percentage, ratio, passage, paper folding,
grammar Easy 15
Total 65 100
Faculty Feedback 13 MSQs level of questions Medium
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GATE 2021 Examination* (Memory Based)
Computer Science Engineering
Test Date:13th Feb 2021
Test Time: 09:30 am to 12:30 pm
Stream Name: Computer Science Engineering
General Aptitude
1. If the ratio of boys and girls in a class is 7:3. Then which of the values possibly be the total
number of students.
(A) 50
(B) 21
(C) 37
(D) 73
[Ans. A]
2. We have two rectangular sheet paper M and N of dimension 6 cm × 1cm each sheets is rolled
to form an open cylinder by bringing two short edges of the sheet together. Sheet N is cut into
equal square patches and assembled to form the largest possible closed cube. Assuming the
ends of cylinder are closed the ratio of the volume of the cylinder to that of cube is
(A) 3/π
(B) 9/π
(C) 3π
(D) π/2
[Ans. B]
3. There are five bags each containing identical sets of ten distinct chocolates. One chocolate is
picked from each bag probability that at least two chocolate are identical is ______________.
(A) 0.6976
(B) 0.3024
(C) 0.4235
(D) 0.8125
[Ans. A]
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4. (i) Everybody in the class is prepared for the exam.
(ii) Baby invited Danish to his home because he enjoys playing chess
Which is correct observation about the two
(A) (i) is grammatically correct (ii) is unambiguous
(B) (ii) grammatically correct (ii) ambiguous
(C) (i) grammatically incorrect (ii) ambiguous
(D) (i) grammatically incorrect (ii) unambiguous
[Ans. B]
5. ____________ is to surgery as writer is to ___________
Which of the following option maintains a similar logical relation in above sentence.
(A) medicine, grammar
(B) hospital, library
(C) plan, outline
(D) doctor, books
[Ans. D]
6. A polygon is convex if, for every pair of points, P & Q belonging to the polygon. The line
segment PQ lies completely inside or on the polygon.
Which one of the following is not a convex polygon?
[Ans. A]
(A)
(B)
(C)
(D)
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7.
Item Cost Profit M.P P 5400 - 5860 Q - 25 10000
Statistics of cost of item P to cost of Q is 3: 4 discount is calculated as the difference between
M.P & S.P. the profit percentage is calculated as the ratio of the difference between S.P and
cost to the cost (profit % =S.P−cost
cost× 100) the discount on item Q, as a percentage of its
marked price is ____________.
(A) 12.5
(B) 10
(C) 25
(D) 5
[Ans. B]
8. All bacteria are micro____________.
Given below two statements 1 & 2 and two conclusions I, II
S1: All bacteria are micro organisms
S2: All pathogens are micro organisms
CI: Some pathogens are bacteria
CII: All pathogens are not bacteria
Based on the above statements and conclusions, which one of the following option is logically
correct?
(A) Only conclusion II is correct
(B) Only conclusion I is correct
(C) Either conclusion I or II is correct
(D) Neither conclusion I nor II is correct
[Ans. C]
Technical
1. limx→−3
√2x+22 −4
x+3
(rounded to two decimal places)
[Ans.*] Range: 0.25 to 0.25
2. Given [A] = [
0 1 1 11 0 1 11 1 0 11 1 1 0
]
Largest eigen value of the matrix is ____________.
[Ans. *] Range: 3 to 3
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3. Representation of a number in base 3 is 210. What is its hexa decimal representation?"
[Ans. *] Range: 15 to 15
4. A graph g contains 8 vertices, and 5 faces find the number of edges?
[Ans. *] Range: 11 to 11
5. "G is group with order 8.
H is subgroup of G
1<=|H|<=6 then which is true
(A) Both G and H cyclic
(B) G cyclic H not cyclic
(C) G not cyclic H cyclic
(D) None cyclic
[Ans. C]
6. Consider 3 process A, B, C all arrived at time zero, with respective burst time 10, 20, 16. The
average waiting time with non-Preemptive SJF S
[Ans. *] Range: 12 to 12
7. True or False
1. The SLR (1) grammars are unambiguous and there are some unambiguous grammars
which are not SLR (1)
2. There exist at most O(n3) algorithm to parse the CFG grammar sat
(A) 1 and 2 both are true
(B) Only 1 is true
(C) Only 2 is true
(D) Neither 1 nor 2 is true
[Ans. A]
8. If PQR = 000 initially, then what are the next three states?
[Ans. *]011, 101, 000
R T T T
P̅
Q P
Q̅ R̅
CLK
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9. Suppose a database system crashes again while recovering from a previous crash. Assume
check pointing is not done by the database either during transaction or during recovery.
Which of the following are true?
(A) System can recover any further
(B) The same undo and redo list will be used while recovering again
(C) All the transaction that are already undone and redone will not be recovered again
(D) the database will become inconsistent
[Ans. B]
9. Let ri(Z) and wi(Z) denotes read/write operations respectively on a data item Z by a
transaction Ti Consider the following 2 schedule.
S1: r1(X)r1(Y)r2(X)r2(Y)w2(Y)w1(X)
S2: r1(X)r2(X)r2(Y)w2(Y)r1(Y)w1(X)
(A) S1 and S2 are non-conflict serializable
(B) S1 and S2 are conflict serializable
(C) S1 is conflict serializable and S2 is non-conflict serializable
(D) S1 is non-conflict serializable and S2 is conflict serializable
[Ans. D]
10. A relation r (A, B) in a relational database has 1200 tuples. The attributes A has integer values
ranging from 6 to 20 and the attribute B has integer values ranging from 1 to 20. Assume that
the attributes A and B are independently distributed. The estimated number of tuples in
output of σ(A>10)or (B=18) r
11. Consider the following relation or R, P, Q, S, T, X, Y, Z, W with the following function
dependency PQ → X, P → YX, Q → Y, Y → ZW
Decompose into D1 and D2
D1: R = (PQST, PTX, QY, YZW)
D2: R = (PQS, TX, QY, YZW)
Which of the following options is correct?
(A) D1 is lossy decomposition and D2 is lossless decomposition
(B) D1 is lossless decomposition and D2 is lossy decomposition
(C) D1 and D2 are lossy decomposition
(D) D1 and D2 are lossless decomposition
[Ans. D]
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12. The following relation records the age of 500 employees of the company, where emp NO
(indicates employee number) is the key.
emp Age (emp NO, age) consider the following relational algebra expression
πemp NO(emp Age) ⋈(age>age) ρemp No 1,age1(emp age)
(A) Employee number of those whose age is maximum
(B) Employee number of only those employee whose age is more than the age of exactly one
other employee
(C) Employee number of those employee whose age is not minimum
(D) Minimum
13. The lifetime of a component of a certain type is a random variable whose probability density
function is exponentially distributed with parameter 2. For a randomly picked component of
this type, the probability that its lifetime exceeds the expected lifetime (two decimal places) is
____________.
[Ans. *] Range: 0.30 to 0.40
14. S1: There exist random variable x and y such that
[(E[x − E(x))(y − E(y))]2
= Var (x) Var(y)
S2: For all random variables x and y
Cov [x, y] = E[|x − E(x)||y − E(y)|] correct?
(A) S1 & S2 = False
(B) S1 → True, S2 → False
(C) S1 & S2 → True
(D) S1 → False, S2 → True
[Ans. *]
15. A: (p ⋀(∼ p ⋁ q) → q)
B: q → (p ⋀ (∼ p ⋁ q)
(A) Both True
(B) A is True & B is not True
(C) A is False & B is True
(D) Both False
[Ans. B]
16. Main memory size 232 bytes. It uses direct mapping and cache memory 32K bytes. The block
size is 64 bytes. What is the number of bits used for TAG.
[Ans. *] Range: 17 to 17
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17. Which of the following standard C functions invoke a system call when executed with a single
thread in UNIX/LINUX OS?
(A) Malloc
(B) Calloc
(C) Exit
(D) Sleep
[Ans. *]
18. The array is already sorted. And options are.
(A) Insertion
(B) Merge
(C) Selection
[Ans. B]
19. 10n , 10log n , nn ascending order asymptotic notation order.
20. Which is not recursive
M is an automation
(A) L(M) is a pda such that Lϵϕ
(B) L(M)is a pda such that Lϵσ∗
(C) L(M)is dfa Lϵσ∗
(D) L(M) is a dfa Lϵϕ
[Ans. *]
21. M is a TM, then
L(M) is a Turing machine which takes at least 2021 steps on all inputs
L(M) is a Turing machine which takes at least 2021 steps on some input Q
(A) L1 decidable, L2: undecidable
(B) L1 undecidable, L2: undecidable
(C) L1 decidable, L2: decidable
(D) L1 undecidable, L2: decidable
[Ans. C]
22. Which of the following will not be recursive CFL?
(A) R. L ∙ CFL
(B) RL ∪ CFL
(C) RL ∩ CFL
(D) RL − CFL
a∗b∗
(anbm|n, m ≥ ,1)
[Ans. D]
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23. 23, 32, 45, 69, 72, 73, 89, 97
(A) Merge-Sort
(B) Quick-Sort
(C) Insertion-Sort
(D) Selection-Sort
[Ans. C]
24. The Boolean function (X̅ + Y̅ + Z̅)(X + Y̅)(Y + Z̅) is equivalent to?
25. S1: Function calling sequence is follows pre-order
S2: Function return follows post-order
Which of the following is true?
(A) S1 only correct.
(B) S2 only correct.
(C) S1 and S2 both are correct.
(D) S1 and S2 both are incorrect.
[Ans C]
26. f1 = 10n, f2 = nlog n, f3 = n√n
[Ans. *]
27. Z be an array: defined such that
Z[i] = 1 for 0 ≤ i ≤ 9
Then the function
function (int array [10], int n, int x)
{
int array; int count, var;
int var = 0;
int Total = array [var];
for (var = 1; var ≤ n − 1; var + +)
{total = total ∗ x + array[var];
}
return total;
}
Called by parameters : function (Z, 10, 2) =?
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28. True or false?
A. The SLR (1) grammars are unambiguous and there are some unambiguous grammars
which are not SLR (1)
B. There exist at most O(n3) time for algorithm to parse the CFG grammar.
[Ans. A] Both statements are correct
More questions will come.
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